Artificial line



.Hume 24 R. S. HOYT ARTIFICIAL LINE Filed Nov. l1

1919 3 Sheets-Sheet l 4l /Z INVENTOR.

g ATTORNEY me 24, 1924. f 1,498,915

R. s. HoYT ARTIFICIAL LINE Filed NOV. ll 1919 3 Sheets-Sheet 2 [YINVENToR.

A TToRNEY Fume 24 19.24.

R. S. HOYT ARTIFICIAL LINE Filed Nov. 1l 1919 3 Sheets-Sheet 3 6.INVENTOR.

' k.. ATTORNEY Patented June 24, 1924.

STATES lgi PATENT OFFICE,

RAY S. HOYT, OF RIDGEWOOD, NEW JERSEY., ASSIGNOR T0 AMERICAN TELEPHONEAND TELEGRAPI-I COMPANY', A CORPORATION 0F NEW YORK ARTIFICIAL LINE.

Application filed November 11, 1919. Serial No. 337,347.

To all whom it may concern Be it known that I, RAY S. HoY'r, residing atRidgewood, in the county of Bergen and State of New Jersey, haveinvented certain Improvements in Artificial Lines, of which thefollowing is a specification.

This invention relates to an artificial line for simulating theimpedance of a transmission line. More particularly, it relates to anartificial line comprising two main portions: a fundamental artificialline for simulating the impedance that an actual line would have ifdevoid of wire-resistance; and a supplementary artificial line for similating the increase produced in the impedance of said actual line by itswireresistance.

For brevity in what follows, this increase in the impedance of a linecaused by its wire-resistance will be termed the excess impedance, or,more precisely, the excess characteristic impedance, since thisinvention is concerned primarily with lines that are long or at leasteffectively long.

The form ofthe fundamental artificial line and also the method ofproportioning it, depend on the type of the actual line involved (smoothline or periodically loaded line). For instance, in the case of a smoothline, the requisite fundamental artificial line is merely a constantresistance; while in the case of a loaded line the requisite fundamentalartificial line consists in general of a combination of severaldifferent elements (resistance, inductance, capacity) as fully setforth, for instance, in my previous patents on artificial lines Nos.1,124,904 and 1,167,693 and in my pending application Serial No.309,633, filed July 9, 1919, which disclose various forms of suchfundamental artificial lines and the corresponding methods ofproportioning.

On the other han'd my supplementary artificial line herein described hasthe same form and the same method of proportioning for all existingtypes of actual lines, and

` is therefore universally adaptable for sup plementing any of theabove-cited or any other suitable forms of fundamental artificial lines.The need for a supplementary artificial line of this character hasarisen particularly in connection with recent re` peater developmentwhere, to admit of large gains without singing, the artificial lines.must simulate with high precision over an extremely widefrequency-range the impedance characteristics of the transmission lineswith which they are associated, the types of artificial lines heretoforeused having been found inadequate for the lower frequencies of therange.

My invention may readily be understood from the following description,reference being had to the accompanying drawings 'in which Fig. 1 is adiagram of one form of my supplementary artificial line; Fig. 1A is adiagram illustrating the employment of this .forni of supplementaryartificial line to supplement any type of fundamental artificial line,the combination thus constitutingr a complete artificial line; Fig. 2 isa plot of the impedance characteristics of smooth lines; and Figs. 3 and4 are charts for use in evaluating the requisite constants of mysupplementary artificialline for any specific case.

As prerequisite to an adequate understanding of the proportioning anduse of my supplementary artificial line the exact nature and magnitudeof the above-mentioned excess characteristic impedance will now beelucidated, after which the supplementary artificial line itself will befully treated.

It is fairly well-known that the character' istic impedance of anefficient telephone transmission line, over most of the telephoniefrequency-range, depends mainly on its inductance and capacity and onlyslightly' on its wire resistance. Hence the excess characteristicimpedance of such a line is relatively small; in fact, for most of thelines and frequency-ranges employed in practice until recently, theexcess characteristic impedance has been either entirely negligible, orelse small enough to be sufficiently simulated by means of a merecondenser (or, at most, by a condenser in series with a very smallinductance).

Recently, however, a more precise simulation of the excesscharacteristic impedance has become necessary; partly because of theemployment of small gauge and therefore less efficient lines (renderedpossible by repeater developments), and partly because of a need forextending the frequency-range to lower frequencies-the excesscharacteristie impedance being greater for lines of low efliciency thanfor lines of high efficiency, and for any given line increasing sistanceand n its excess characteristic reactance. Then, by the definition ofexcess characteristic impedance, we have czK-K (l) so that m=M-M (2) andnzN-N (3) In the following analysis of the excess vcharacteristicimpedance it suiiices to treat only smooth lines explicitly (a smoothline being one whose constants are all uniformly distributed), becausethe excess characteristic impedance of a periodically loaded line isapproximately the same, over most of the frequency-range below thecritical `frequency of the loaded line, as the excess characteristicimpedance of a smooth line having the same total constants as the givenloaded line. It will thus be 'seen that my supplementary artificial lineherein disclosed is applicable to periodically loaded lines (includingperiodically loaded cables), as well as to smooth lines (includingnon-loaded cables, non-loaded aerial lines, smoothly loaded cables, andsmoothly loaded aerial lines).

For a smooth line possessing inductance L, capacity C, and resistance RLper unit length, the value of K is given by the wellknown formulawherein p denotes 21: times the frequency f, and z' denotes theimaginary operator 1/ 1 Since for any given line we are concerned withthe impedance as a function of the frequency f, the study of the above`formula For use below, it may be here noted thatl (4) for K will besimplied and at the same time rendered more comprehensive by introducingthe two symbols g and F defined by the equations i (Thus the parameter gis interpretable as being the characteristic impedance that the 75 linewould have if devoid of wire-resistance.) Hence the excesscharacteristic 1mpedance cIK-K is given by the formula To secureformulas for the two components m and n of and also formulas for the twocomponents M and N of K, it is necessary to carry out the indicatedroot-extraction to obtain the real and imaginary components of'thiscomplex quantity 1 fi/F which occurs in the formula (10) foi` k and 90in the formula (7) for K. Performing this operation with reference to(7), the resistance and reactance components and N of the characteristicimpedance K will be found to have the values given by the formulae M:t/l -i-Fz (l1) g. 2F Ny l 2F (12) g :5F F1a/1+@ whence the excesscharacteristic resistance mzM--M and the excess characteristic reactancen--N-N are given by the formulas which is obviously greater than unityfor all positive values of F.

To furnish a clear and exact idea of how` the quantities M, N, m, ndepend on the frequency f, Fig. 2 gives graphs of M/ -N/g, m/g, -n/g asfunctions of F-wliich, for any fixed line, is proportional to f, it willbe remembered. These graphs bring out the fact-indicated by formula(15)-that the excess characteristic resistance m is, at all values of F,smaller than the negative excess characteristic reactance 01; in factthat m is much smaller than *n except at very small values of F, m thereapproaching -n. The graphs show also that m and-n are both smallcompared with g at the larger values of F but that they both increasewith decreasing F until at small values of F they become comparable withg, and at still smaller values of F they even exceed g.

Since F:(21cL/R)f, the curves of Fig. 2 show also that, at any fixedfrequency f the excess characteristic impedance of any given line (L andC fixed) increases as R increases-the above formula for F showing thatincreasing R has the same eifect as decreasing f.

Thus it is seen that ordinarily the` increase produced in thecharacteristic impedance of .a transmission line by its wire-resistanceis mainly an excess characteristic reactance, which may be very large atlow frequencies but rapidly decreases with increase of frequency,ordinarily becoming negligible at high and at medium frequencies andoften at low frequencies even. In fact, for the frequency-ranges and thelines employed in practice until recently, the excess characteristicresistance has .been entirely negligible; while the excesscharacteristic reactance,l though not always negligible-and even ratherlarge in some caseshas been simulated sufliciently closely by means of amere condenser..l A

Having thus furnished an exact and comprehensive idea of the nature andmagnithe above-defined excess impedance very closely over a wide rangeof frequencies; whence the total impedance of the actual line can besimulated by the complete artiicial line, represented by Fig. 1A,consisting, of said supplementary artificial line connected in serieswith the requisite fundamental articial line, whose impedance is theredenoted by Z4. For the purpose of eva-luatin the elements of saidsupplementary artificial line, I may regard the same as consisting oftwo parts serially connected between the two terminals t, t. Part 1,which is the major part, comprises a resistance element R1 and acapacity element C1 in serieswith each other, and a capacity element C2in shunt therewith; while part2 comprises merely a resistance elementR3. The artiicial line is thus made up of four impedance-elements only.The resultant impedance of the combination, when the elements areproportioned as hereinafter set forth, with reference to the constantsof the contemplated actual line, closely simulates the excesscharacteristic impedance of said actual line over a wide range offrequencies.

Let ZzX-l-Y denote the impedance of the entire supplementary artificialline, between the terminals t, t, represented by F ig. 1; X and Y thusdenoting respectively the resistance component` and the reactancecomponent of said impedance Z. Then To secure the desiredimpedance-simulation the impedance elements R1, C1, C2, R3 of thesupplementary artificial line must be proportioned with reference to thegiven values ofr the constants L, C, R of the actual line. There arevarious procedures that might be followed in arriving at suitable (O1'l' Cz) 2 'l' (B10102202 values of the impedance-elements R1, C1, C2,

the parameters S, T, 7, C21 defined by the following equations:

whence the constants R1, C1, C2, R3 of the supplementary artificial linein terms of the parameters S, T, 7, C21, and in terms of the constantsL, C, R of the actual line, are

ST ,/L-C Cl:0210+020 (24) C, ST @C `(25) T E RFT@ 26) artificial line isto simulate by its impedance ZzX-l-Y the excess characteristic impedancevzm-l-ifn, of the actual line, the most fundamental design-formula isevidently and the proportioning of the supplementary artificial line isto be such as to fulfill this equation as closely as may be. Since theimpedances are complex, this equation implicity contains the twofundamental design-formulae Xzm (30) i Yzn (31) or, what is equivalent,

X/gIm/g (32) Y/gIn/g (33) Since the main part of the design-workconsists in evaluating the parameters S, T, r, C21 characterizing thesupplementary artiicial line, in terms of the known constants of theactual line, the quantities occurring in the fundamental design-formulae(30) and (31) must next be expressed in terms of the above-mentionedparameters. This can be done by means of (13), (14), (27), (28); and,for design-purposes, the two resulting relations can be written mostconveniently -in the forms where the functions on the right-hand sideshave the following explicit meanings In these formulae the quantity F,which for any fixed line is by (6) proportional to the frequency f, isto be regarded as the independent variable, since we are concerned withimpedance-simulation over a wide frequency-range; and the remainingquantities are to be treated as parameters.

Referring now to the two design formulae (34) and (35) itlwill berecalled that they were established from the assumption that theimpedance of the supplementary artificial line is equal to the excesscharacteristic impedance of the actual line; in fact they are nothingmore norless than indirect statements of such assumed equality.

p Now, 'r and C2, are constants of the supplementary artificial line (1-being proportional to the resistance-element R`and C21 being the ratioof two capacity-elements) Hence, mathematically stated, the prob em isreduced to determining what values of the parameters S and T will render1- and -1C21+ST/2, expressed by (34) and (35), as nearly as possibleindependent of F 'over the contemplated F -range, for positive values of7' and C21. are discussed below). V

The evaluation of the parameters for specific cases can be accomplishedby means of the sets of curves furnished herewith in Figs. 3 and 4. Fig.3 gives two superposed sets of curves; solid curves, which are graphs of41 (F,T) as uonction of F with T as parameter; and dashed curves, whichare graphs of qb (F,S) as function of F with S as parameter. Similarly`Fig. 4 ives two superposed. sets of curves; soli curves,

(Negative values lof 7' which are graphs of 0 (F,ST) as function of Fwith the product ST as parameter; and dashed curves, which are graphs of(RS) as function of F with S as parameter. (Except for complexity andresulting confusion, the gb, 1/1 and 0 curves might evidently be plottedin a single diagram as one three-fold set of curves).

To evaluate the parameters for any specific case, the sets of curves inFigs. 3 and 4 are to be inspected, over the particular F- rangecontemplated in said specific case, with the object of selecting acertain qbcurve common to the two sets of curves; and in Figs. 3 and 4,respectively, selecting a 1]/- curve and a -curve that are approximatelyparallel to the common curve, and moreover are such that the value of STfor the 0curve is equal to the product of the values of S and T for theqS-curve and the lp-curve; the selection, moreover, to be such as toyield a positive value for C21 when computed from (35).

When my supplementary artificial line is to be used independently, i.e., as an addition to an already existing artificial line and withoutchange in the elements of either, it is necessary that the chosenlpcurve be not below the chosen (jb-curve in order that 7', and henceR3, shall not be negative. This is not always necessary, however, whenthe supplementary artificial line is not to be used independently, forthen the remaining artificial line in series with the supplementaryartificial line can sometimes be so proportioned as to absorb a.negative R3-element; this being accomplished in the design by reducingby an amount equal to --R3 the resistance component of the impedance ofthe remaining artificial line. (In the case of non-loaded cables, thedesign can often be so carried out that the negative R3-element will beexactly absorbed, whence then the resulting total artificial line willconsist merely of the principal part (R1,C1,C2) of the supplementaryartificial line represented in Fig. l).

Although the sets of curves given in Figs. 3 and 4 cover a lfairly widerange of practical cases, no attempt has been made to render themsufficiently extensive to cover all cases that might arise; theirpurposes here being mainly illustrative. For cases falling outside oftheir range they can be readily extended by means of formulae (36),(37), (38). Moreover, for illustrative purposes, it has sufficed tp plotthem rather sparsely, whence they can serve only for approximateevaluation of the parameters, more refined evaluations requiring moredensely plotted sets for values of the parameters in the neighborhoodsof the values first determined approximately.

From alttle studv of the design-charts of Figs. Sand 4, it will be seenthat in many cases there vwill be a considerable range in the choice ofthe parameters and hence a considerable range in the choice of values for the constants of the artificial line to slmulate approximately theimpedance of the specified actual line over the preassignedfrequency-range. By taking advantage of this fact, it is often possibleto arrive at constants having values more suitable for commerclalapplications than would otherwise be obtained.

.As a simple example illustrating the apphcation of my invention, let itbe required to construct an artificial line for closely simulating, overthe frequency-range extending from )c2200 to f=2500 cycles per second,the l impedance of a long smooth transmission line having the followingspeclfications: An aerial line consisting of two parallel #12 N BS,gauge copper wires having an inductance L:0.00367 henrys per mile, acapacity C:0.00835 106 farads per mile, and a resistance R:l0.4 ohms permile.

If this line were devoid of wire-resistance (that is, if R=O) the lineimpedance at all frequencies would be equal merely to w/L/C 663 ohms,

and hence would be exactly simulatable by a mere constant resistance of663 ohms, which therefore is in this example the particular value of Z4in Fig. 1A. As explained above,- the impedance of the actual line (R notzero) exceeds this limiting value w/L/C by an amount, there termed theexcess impedance, whichit'is the province of the supplementaryartificial line of my present invention to simulate; such supplementaryartificial line therefore to be connected in series with Z4, thecombination thus constituting the required complete artificial line forsimulating the total impedance of the specified actual line.

As the first step in the proportioning of the supplementary artificialline, the values of L and R are to be substituted in equation (6). Itwill be thus found that F:.0.00222 f, and hence that the preassignedf-range of 200 to 2500 corresponds to an F-range of 0.444 to 5.55-whichis therefore the F-range over which impedance simulation is required.Next, inspecting over this particular F-range the sets of curves inFigs. 3 and 4 in the manner above described for evaluating theparameters S and T it will be found by interpolation that suitablevalues of S and T are S=2.3, T:1.7, and hence ST 3.9. For these valuesof S and T, the [1f-curve and t-curve are substantially coincident. sothat by (34) we may regard 1' as equal to zero. Moreover, the H-curveand curve also are substantlally co1nc1- dent, so that by (35) we findthat 021:095.

Thus, summarized, the parameters of the supplementary artificial linehave the values determining the simulative precision of the completeartificial line, as represented in per cent by the function d=100\Z-K\/IKI gave the following values of d (from which additional values can beobtained by plotting a curve, if desired) f, Cycles per d, Per second.cent. 200 1.78 300 .54 500 .55 800 .37 1200 .20 1600 .13 2000 .09 2300.06 2500 .06

Thus, over most of the contemplated frequency-range of 200 to 2500cycles per second, the complete artificial line of this eX- ample doesnot differ from the actual line in impedance by more than about one-halfof one per cent; while its greatest departure (occurring at f=200) isless than two per cent. As above remarked, in the designwork of thisillustrative example the parameters S and T-which determine (indirectly)the constants of the supplementary artificial linewere evaluated by amere lnspectional process of interpolation inthe rather sparse sets ofcurves furnished vin Figs. 3 and 4; that is, S and T were evaluatedwithout recourse to any curves more densely plotted, and withoutrecourse to any tentative computations of the precision. By suchrecourse, higher and more uniform simulative precision could be securedif desired, but the precision attained in this exam le without suchrecourse is sufficiently good for most applications.

Althoughonly one form of apparatus embodying this invention is shown anddescribed herein it is readily understood that various changes andmodifications may be made therein within the scope of the followingclaims without departing from the spirit and scope of the invention.

What I claim is: Y 1. An artificial line comprisin resistance andreactance elements designe and combined so that the impedance over awide range of frequencies is substantiallyI the same as the precomputedexcess impedance of an actual line.

2. An artificial line comprising a plurality of impedance elements whosevalues are computed as functions dependent upon the resistance componentof the impedance effect caused by the resistance of the conductors of anactual line.

3. An artificial line for simulating that part of the impedance of anactual line which is caused by the resistance of its conductors, saidartificial line comprising a plurality of impedance elements whosevalues are determined by a computation based on the resistance andreactance components of that part of the impedance due to the resistanceof the line conductors.

4. An artificial line comprising a plurality of portions connected inseries with each other, one of said portions being comprised of aplurality of parallel branches, and impedance elements in said branchesand in said other portions, some of said impedance elements beingresistances and some of them being reactances, the values of saidelements being determined by a computation based on the variation over aWide range of frequencies of the impedance effect due to the esistanceof the conductors of an actual ine. 4

5. An artificial line comprising a plurality of portions connected inseries with each other, one of said portions comprising a resistanceelement; another of said portions comprising a plurality of parallelbranches, one branch comprising a capacity element, another branch aresistance element in series with a capacity element, the values of saidelements being determined by a computation based on the variation over awide range of frequencies of the impedance effect due to the resistanceof the conductors of an actual line.

6. An artificial line which consists of a plurality of portions, onehaving its impedance elements computed to simulate over a wide range offrequencies the impedance of a line assuming the line conductors to haveno resistance, and another having its impedance elements computed tosimulate over a wide range of frequencies both the resistance andreactance components of the impedance effect due to the actualresistance of the said line conductors. i

7. An. artificial line which consists of two portions, one simulating agiven line on the assumpution that its ohmic resista-nce is zero, andthe other computed as a function of the constants of the given line tosupply the impedance defect involved in the `assumption on which thefirst mentioned portion of the artificial line is based, said otherportion sii meseta W;

comprising resistance an reactance elements tion by means of a networkcomputed as a 1n combination.

` function of the constants of the given line. 8. The method ofbalancing the impedance ln testimony whereof, l have signed my no ofaline which consists in balancing itsimname to this speciication this10th day o 5 pedanceon the assumption that its ohmlc re- November,1919.'

sistanco is zero, and then balancing out the impedance defect involvedin that, assump` RAY S 0

